Algebra I: 1001 Practice Problems For Dummies (+ Free Online Practice). Mary Jane Sterling

      668.

      669.

      670.

      671.

      672.

      673.

      674.

      675.

      676.

677.

      678.

      679.

      680.

      681.

      682.

      683.

      684.

685.

Chapter 16

      Reining in Radical and Absolute Value Equations

      Aradical equation contains at least one term that’s a square root, cube root, or some other root. When solving radical equations, you apply a method that’s effective but comes with a built-in error possibility; you may find (and need to recognize) extraneous solutions. You need to rewrite absolute value equations to solve them. The solutions of the rewrites are then the solutions of the original equation.

The Problems You’ll Work On

      Here’s just a sampling of the radical things you work on in this chapter:

       Rewriting equations with only two terms and squaring both sides to solve

       Squaring both sides of an equation when starting with three terms

       Dealing with more than one radical term

       Catching extraneous solutions

       Graphing absolute value statements for clarity

       Solving absolute value equations after writing corresponding equations

       Checking for nonsense answers

What to Watch Out For

      Here are a few things that may rock your boat, so be on the lookout:

       Squaring binomials correctly and not forgetting the middle term

       Factoring statements containing radicals correctly

       Checking for extraneous solutions by using the original equation, not the version changed in the process

       Catching impossible situations in initial absolute value equations

Solving Basic Radical Equations

      686–689 Solve each radical equation by squaring both sides.

      686.

      687.

      688.

      689.

Checking for Extraneous Roots

      690–697 Solve the radical equations by squaring both sides; check for extraneous solutions.

      690.

      691.

      692.

      693.

      694.

      695.

      696.

      697.

Squaring Both Sides of Equations Twice

      698–701 Solve each radical equation by squaring both sides of the equation twice.

      698.

      699.

      700.

      701.

Solving Radicals with Roots Other Than Square Roots

      702–703 Solve the radical equations.

      702.

      703.

Solving Absolute Value Equations

      704–713 Solve each absolute value